Draw a tree diagram to represent the following scenario. You choose a random letter from the word SANDWICH. How many possible outcome are there?

Answer:

a

Step-by-step explanation:

(3/4) to the power of 2 means to multiply it by itself and so, 3/4 times itself is 9/16

Answer:

Step-by-step explanation:

Hello

[tex]\large\displaystyle\text{$\begin{gathered} \sf Apply \ the \ third \ exponent \ rule-: \bigg(\dfrac{x}{y}\bigg)^m=\dfrac{x^m}{y^m} \end{gathered}$}}[/tex]

Solve-:

[tex]\large\displaystyle\text{$\begin{gathered} \sf \bigg(\dfrac{x}{y}\bigg)^2= \dfrac{3^2} {4^2} =\boxed{\sf{\frac{9}{16}}} \end{gathered}$ }}[/tex]

[tex]\pmb{\tt{done \ !!}}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

The flow rate of the given fluid in the pipe is gotten as; 3/2 liters per minute

We are told that a pipe fills 11/15 liters in 22/45 minutes.

Now, to get the flow rate of this pipe, we will use the formula;

Flow rate = Quantity of fluid/Time

Thus;

Flow rate = 11/15 ÷ 22/45

⇒ 11/15 * 45/22

⇒ 3/2 liters per minute

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Step-by-step explanation:

Answer:

$1.90

Step-by-step explanation:

16.80 - 1.60 = 15.20, since we are finding the price of each bottle of juice.

1) Set up and equation equated to 15.20.

8x = 15.20

x = 15.20/8

x = 1.90

Therefore, each bottle of juice costs $1.90.

Answer:

C

Step-by-step explanation:

Here we can see this is a bit of an trial and error, let's go through the options individually.

To find whether the ordered pair satisfies the equation, we will substitute x and y into the equation. To have the ordered pair to satisfy the equation, the value must be 7.

A) Given x = -5 , y = 3,

[tex]-5x+3y= - 5(-5)+3(3)\\=25+9\\= 34\\34 \neq 7[/tex]

Therefore this pair does not satisfy the equation.

B) Given x = 2, y = -1,

[tex]-5x+3y = -5(2)+3(-1)\\= -10-3\\=-13\\-13 \neq 7[/tex]

Therefore this pair does not satisfy the equation.

C) Given x = 7, y = 14,

[tex]-5x+3y = -5(7)+3(14)\\= -35 + 42\\= 7[/tex]

Therefore this pair satisfy the equation.

D) Given x = -2, y =[tex]-\frac{13}{5}[/tex],

[tex]-5x+3y = -5(-2)+3(-\frac{13}{5} )\\=-10-\frac{39}{5} \\=-17.8 or -17\frac{4}{5} \\-17.8\neq 7[/tex]

Therefore this pair does not satisfy the equation.

The area of sector POR is approximately equal to 68.76 square centimeters, and the perimeter of sector POR is approximately equal to 34.92 centimeters.

In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the length of an arc formed by a circle is given by:

Length of an arc = 2πr × θ/360

Substituting the given parameters into the formula, the radius of this circle is given by;

12 = 2 × 3.142 × r × 60/360

12 = 2 × 3.142 × r × 1/6

72 = 6.284r

Radius, r = 72/6.284

Radius, r = 11.46 centimeters.

Now, we can calculate the area of sector POR:

Mathematically, the area of a sector can be calculated by using this formula:

Area of sector = πr² × θ/360

Where:

Substituting the given parameters into the formula, we have;

Area of sector = 3.142 × 11.46² × 60/360

Area of sector = 3.142 × 131.3316 × 1/6

Area of sector = 68.76 square centimeters.

Next, we would calculate the perimeter of sector POR:

Perimeter of sector POR = 2r + Length of an arc

Perimeter of sector POR = 2(11.46) + 12

Perimeter of sector POR = 22.92 + 12

Perimeter of sector POR = 34.92 centimeters.

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Answer:

9 m²

Step-by-step explanation:

s = half the perimeter = (a+b+c)/2

the perimeter in our case is

a+b+c = 16

so, s = 16/2 = 8

and the sides are

7 m

6 m

16 - 7 - 6 = 3 m

therefore, we get

area = sqrt(8(8-7)(8-6)(8-3)) = sqrt(8×1×2×5) = sqrt(80) =

= 8.94427191... ≈ 9 m²

Answer: the answer is b

Step-by-step explanation:

The system of inequality is y > 3 and 3x -2y < 1 these are the inequalities that represent the region.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have a line showing the graph.

First, we have to calculate the equation of the line:

The horizontal line:

y = 3

The region represents the inequality:

y > 3

Second inequality line:

[tex]\rm \dfrac{x}{-2}+\dfrac{y}{3} < 1[/tex]

3x -2y < 1

Thus, the system of inequality is y > 3 and 3x -2y < 1 these are the inequalities that represent the region.

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The expression that is equivalent to -9/6 is = 9/-6. That is option A.

Fraction is represented by a numerator and a denominator which can be either positive or negative.

From the fraction given, -9/6. The numerator is 9 while the denominator is 6.

The expression that is equivalent to -9/6 is = 9/-6 and not -9/-6 because the negatives are cancelled out.

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Answer:

x = 4

Step-by-step explanation:

the two angles you see are alternate exterior angles, meaning they are equal to eachother.

32x + 2 = 33x - 2

subtract so that x is on one side. 33 - 32 = 1, so the equation would be

2 = x - 2

add 2 to both sides.

4 = x

hope i helped.

Answer:

x = 16x

Step-by-step explanation:

32x divided by 2 equals 16x

33x minus 2 also equals 16x

Since the numbers are the same for both equations X equals 16x

30 mph would be a safe speed for you to drive.

Collisions are much more likely to occur when one driver travels greater speedy or more slowly than the alternative motors on the road. You have to input a throughway at or near the velocity of visitors except if the speed of site visitors exceeds the prison speed restrict.

A pedestrian has a 90 percent threat of survival if hit by a vehicle transferring at 30 km ph (18.64 mph). This decreases to 70 percent at 40 kmph (24. eighty five mph) and much less than 20 percent at 50kmph (31 mph). driving at decreased speeds also enables drivers to stop within a shorter distance.

Retaining high speeds on highways is straightforward, as roads are wider and traffic is usually mild. If there are signs that show a pace restriction of 80kph, use them as a guide and stick near them. it's also an excellent exercise to assess road situations and set your pace thus.

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Using translation concepts, the transformation is defined by:

J. A translation of triangle XYZ to the right.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the orientation of the triangle remains the same, hence it is a translation of the triangle to the right.

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Rejecting the null thesis means that;

There's sufficient substantiation to support the claim that the mean is lesser than 32 long hauls per gallon.

For thesis testing, the first thing to define is the null and indispensable thesis.

In thesis testing, especially one comparing two sets of data, the null thesis plays the devil's advocate and generally takes the form of the contrary of the proposition to be tested. It generally contains the signs = , ≤ and ≥ depending on the directions of the test. It generally maintains that, with arbitrary chance responsible for the outgrowth or results of any experimental study/ thesis testing, its statement is true.

The indispensable thesis generally confirms the proposition being tested by the experimental setup. It generally contains the signs ≠,< and> depending on the directions of the test. It generally maintains that significant factors other than arbitrary chance, affect the outgrowth or results of the experimental study/ thesis testing and affect in its own statement.

For this question, Carter Motor Company claims that its new hydrofoil, the Libra, will total better than 32 long hauls per gallon in the megacity. And since this is talking distance covered per gallon of energy, better means that the new hydrofoil will total further than 32 long hauls per gallon.

So, the null thesis negating this claim would be that there is not significant substantiation to conclude that the normal of the new hydrofoil will be more or lesser than 32 long hauls per gallon.

That is, the new normal will be lower than or equal to 32 long hauls per hour.

And the indispensable thesis will confirm the claim that there's significant substantiation to conclude that the normal of the new hydrofoil will be more or lesser than 32 long hauls per gallon.

Mathematically,

The null thesis is represented as

H ₀ μ ≤ 32 long hauls per gallon

The indispensable thesis is given as

Hₐ μ> 32 long hauls per gallon

So, after the thesis test has been conducted, rejecting the null thesis means accepting the indispensable thesis and its statement that there's significant substantiation to conclude that the normal of the new hydrofoil will be more or lesser than 32 long hauls per gallon.

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The young modulus of a wire with an area of 0.01 m², that strain 6.25 * 10⁻³ if a load of 100N is applied is 16000 N/m²

An equation is an expression that shows the relationship between two or more variables and numbers.

The young modulus is given as:

Young modulus = stress / strain = load / (area * strain) = 100 / (0.01 * 6.25 * 10⁻³) = 16000 N/m²

The young modulus of a wire with an area of 0.01 m², that strain 6.25 * 10⁻³ if a load of 100N is applied is 16000 N/m²

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Considering the given data-set, the dot plot is incorrect for the number 1.

The dot plot shows the number of times each measure appears in the data-set.

In this problem, number 1 appears only twice on the data-set, but has 3 dots, hence it is incorrect, it should be 2 dots.

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Answer:

yes

Step-by-step explanation:

she is right because if he had did as she said it could have been better

See below for the steps to the two-way relative frequency table

The table of values is given as:                                  

Communication Gender  Male         Female    Total

Text                                   150.0           82.0      232.0

Talk                                    72.0            36.0       108.0

Social Media Apps            28.0            32.0      60.0

Total                                   250.0         150.0     400.0

Start by dividing each cell by the column total

                               Male                     Female                  Total

Text                   150.0/250 = 0.6       82.0/150 = 0.55    232/400 = 0.58

Talk                    72.0/250 = 0.288       36.0/150 = 0.24  108/400 = 0.27

Social Media Apps    28.0/250 = 0.112      32.0/150 = 0.21    60/400 = 0.15

Rewrite properly as:

                               Male                Female                  Total

Text                         0.60                0.55                        0.58

Talk                        0.288               0.24                          0.27

Social Media Apps   0.112                0.21                        0.15

Total                             1                       1                              1

The above represents the two-way relative frequency table

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The value of the probability P(AnB) is 0.11

The given parameters are:

P(a|b)=0.55 and P(b)=0.2

The value of P(AnB) is calculated using:

P(AnB) = P(a|b) * P(b)

Substitute the known values

P(AnB) = 0.55 * 0.2

Evaluate the product

P(AnB) = 0.11

Hence, the value of the probability P(AnB) is 0.11

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Answer:

Step-by-step explanation:

f(-2) means that the "x" variable in the equation can be substituted for -2

So, we have

-5(-2) + 12

This equals 10 + 12 = 22

So, the answer is 22

Answer:

200.96 m^2

Step-by-step explanation:

The formula for the area of a circle is πr^2, where r is the radius of the circle and π is approximately 3.14. We know that the diameter is 16 meters, and the radius is always half of the diameter (the diameter connects two ends of the circle, while the radius connects one point to the center). Therefore, the radius of this circle is 8m. Now we have all the information we need. The area of this circle is (3.14)(8)^2 = 3.14*64 = 200.96 m^2 (area is always in squared units)

Answer:

200.96m²

Step-by-step explanation:

Area of a Circle: Pi×r²

where:

pi = 3.14

r = diameter / 2

= 16÷2

= 8

Area = 3.14 × 8 × 8

= 200.96m²

Answer:

3 is the coefficient of m3

Answer:

6

Step-by-step explanation:

2+2+2

Answer:

A. The function is always decreasing

Step-by-step explanation:

we read a graph from left to right, so we can always compare the increase/decrease of a function by seeing how an x value compares with an x value to the left

(I am aware that this paragraph is really confusing)

we can see that as x increases, from -∞ to 0,

y decreases in correspondence

and that as x increases, from 0 to ∞,

y decreases in correspondence also

So, even though the graph doesn't quite look like it, when x < 0; the function decreases, when x > 0; function decreases--so the function is always decreasing

hope this helps!! have a lovely day :)

Rewriting the left hand side,

csc²t - cost sec t

= (1/sin²t)-(cost)(1/cost)

= 1/sin²t - 1

= 1/sin²t - sin²t/sin²t

= (1-sin²t)/sin²t

= cos²t/sin²t

= cot²t

Step-by-step explanation:

assuming this is correct, you can really manipulate either side and you should arrive eventually arrive to same sides. But in this case you usually manipulate the more complex side. So I'll manipulate the left side.

Original Equation:

[tex]csc^2(t)-cos(t)*sec(t)=cot^2(t)[/tex]

Rewrite csc and sec, using the reciprocal identities:

[tex](\frac{1}{sin(t)})^2-cos(t)*\frac{1}{cos(t)}=cot^2(t)[/tex]

multiply cos(t) and 1/cos(t) and also distribute the exponent:

[tex]\frac{1}{sin^2t}-1=cot(t)^2[/tex]

Multiply 1 by sin^2(t)/sin^2(t)

[tex]\frac{1}{sin^2(t)}-\frac{sin^2(t)}{sin^2(t)}[/tex]

subtract the numerator

[tex]\frac{1-sin^2(t)}{sin^2(t)}[/tex]

Pythagorean Identity:

[tex]sin^2(t)+cos^2(t)=1[/tex]

subtract sin^2(t) from both sides

[tex]cos^2(t)=1-sin^2(t)[/tex]

Use this to rewrite the numerator:

[tex]\frac{cos^2(t)}{sin^2(t)}[/tex]

Rewrite using the reciprocal identities:

[tex]cot^2(t) = cot^2(t)[/tex]

The value of expression (m n)(x) for x=-3 by putting x=-3 is -3mn.

Given Expression (m n)(x) and we have to find the value for x=-3.

Expression refers to the combinations of numbers, symbols, variables. It is usually not present in equal to form. It is often solved for finding the overall relationship between variables. It is often expresses quantity of one variable and combination of some material.

The given expression is (mn)(x)

To find the value of expression for x=-3, we have to just put the value of x=-3

mn(x)=(mn)(-3)

=(mn)-3

=-3mn

Hence the value of  expression (mn)(x) for x=-3 is -3mn.

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Answer: f^-1(1) + f(-14) = 20, f^-1(-2) = 10

Step-by-step explanation:

When finding the inverse through a table of functions, we are doing the opposite of a function. For example:

If f(9) = 1, then, let me ask you, what is f^-1(1)? Well, that's just 9! You're basically doing the opposite.

An inverse through a table of functions is basically you trying to figure out what x-value did you input to get the f(x) value. A regular function is you trying to figure out what f(x) value did you get by inputting an x-value.

So, the inverse of f(1) is 9, and the regular function of -14 is equal to 11. We then add. 11+9 = 20.

The inverse of -2, like I said before, is you trying to find out the x value you put to get -2. Well looking at the table, it seems x was 10. Thus the inverse of -2 is 10.

Please find the question attached below.

The equation that models the decrease in water (in gallons) of the fish tank over time (in hours) is y = - 20x + 180.

We know that a linear equation with one variable is one that contains just one variable.

Here we have to find the appropriate equation that models the given chart.

For option A. :

y = - 40x + 140

At x = 2, y = - 40*2 + 140 = - 80 + 140 = 60 =/ 140

So this option is incorrect.

For option B.:

y = - 40x + 180

At x = 2, y = - 40*2 + 180 = - 80 + 180 = 100 =/ 140

So this option is incorrect.

For option C.:

y = - 20x + 140

At x = 2, y = - 20*2 + 140 = - 40 + 140 = 100 =/ 140

So this option is incorrect.

For option D.:

y = - 20x + 180

At x = 2, y = - 20*2 + 180 = - 40 + 180 = 140

So this option is correct.

Therefore, the equation that models the decrease in water (in gallons) of the fish tank over time (in hours) is y = - 20x + 180. So, the last option is correct.

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